ST's VNH2SP30 and VNH3SP30 are right in that ballpark. Pololu has dual and single VNH carrier boards that let you do 30 A max and around 14 A continuous (VNH2 only, VNH3 can do up to 9 A continuous) without a heat sink. If you added a heat sink you could raise the continuous current rating to something closer to the 30 A max.

Well, digikey wells the VNH2s (each IC contains a single H bridge) for a unit price of $10.51 (and VNH3s for 8.26 each), so I suppose you could buy the chip and surface-mount it yourself to a PCB. I'm not sure what other high current H bridges are out there, but I expect the prices would be similar to this. Driving a motor at 14 A continuous is much harder than driving a motor at 1 A continuous.

Hold up, I was reading the data sheet for the VNH3 and VNH2, they both say they can hold 30 amps continuous - does it still require the heatsink when going above 9 amps because it isn't mentioned there?

For you it might require a heat sink before 9 amps. The carrier boards I linked to in my first post cool the chips by acting as a heat sink, allowing them to reach the current levels I listed without overheating. The chip by itself could very well overheat at lower currents.